Import Question JSON

Current Question (ID: 7373)

Question:

$\text{The average molar mass of the mixture of CH}_4 \text{ and C}_2\text{H}_4 \text{ present in the mole ratio of a:b is 20 g mol}^{-1}\text{. When the mole ratio is reversed, the molar mass of the mixture will be:}$

Options:

1. $24 \text{ gram}$
2. $42 \text{ gram}$
3. $20 \text{ gram}$
4. $15 \text{ gram}$

Solution:

$\text{Hint: The average atomic mass of a mixture is the sum of the masses of its compound, each multiplied by its amount divided by the total amount of mixture}$ $\text{Step 1:}$ $\text{Let a mole of CH}_4 \text{ and b mole of C}_2\text{H}_4 \text{ be present}$ $\therefore \text{The average molar mass of mixture} = \frac{a \times 16 + b \times 28}{a + b} = 20$ $\therefore 4a = 8b$ $\text{or} \frac{a}{b} = \frac{2}{1}$ $\text{or} a = 2b$ $\text{On reversing mole ratio b mole of CH}_4 \text{ and a mole of C}_2\text{H}_4 \text{ be present}$ $\therefore \text{The average molar mass of mixture} = \frac{b \times 16 + a \times 28}{a + b}$ $(\text{Now,}) \frac{b}{a} = \frac{1}{2} \quad \frac{b \times 16 + 2b \times 28}{b + 2b} = \frac{72}{3} = 24 \text{ g mol}^{-1}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}